kevin is the most likely scenario
i've ran into this many times on the cat's with the light bar assy's and the multifunction lights.

if you check the ground terminal in the light assy you will find it is loose. They are only riveted onto the ground plate and they do get loose over time causing the bad ground, since the ground in this circuit effects the brake, park and reverse lights it may cause erratic behaviour in any of those circuits.
You can try to remove the rivet and put a screw in it if you want but it generally is wise to just replace the light assy as the labor to repair it cost more than the light and swapping it out.
Also check the wiring in the OHG, there is a plug just inside the OHG that may be corroded. It may be located just at the base of the OHG leg where the harness enters the OHG or at the top where it comes out (all depends on the configuration and model year).